Subgroups — #14643740

Order 2816.

542 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077249	C₂	1	2	yes	maximal
2	#13066493	C₂	1	4	yes	maximal
3	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
5	C₁₁×#431	—	2	2	no	—
6	C₁₁×#431	—	2	2	no	—
7	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
8	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
10	#10622820	C₂²	1	4	yes	—
11	#10622539	—	2	2	no	—
12	#10622539	C₄	1	4	yes	—
13	#10622538	—	2	2	no	—
14	#10622538	C₄	1	4	yes	—
15	#10622537	—	2	2	no	—
16	C₄×#4318	—	2	2	no	—
17	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
18	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
19	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
20	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₁	D₄	1	2	yes	—
28	C₂×C₄²×C₁₁	D₄	1	2	yes	—
29	C₂×#4318	—	2	4	no	—
30	C₁₁×C₄⋊C₈	—	2	4	no	—
31	C₁₁×C₂²⋊C₈	—	2	4	no	—
32	C₄×C₈×C₁₁	—	2	2	no	—
33	C₄×C₈×C₁₁	—	2	2	no	—
34	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
35	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	8	yes	—
36	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
37	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
38	#66867	—	2	4	no	—
39	C₄×C₁₁⋊C₈	—	2	4	no	—
40	#8006	—	11	1	no	maximal, Sylow
41	C₂⁴×C₁₁	C₂×Q₈	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	—	2	4	no	—
43	C₂²×C₄×C₁₁	—	4	2	no	—
44	C₂²×C₄×C₁₁	—	4	2	no	—
45	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
55	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
56	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₁₁	—	2	4	no	—
58	C₂×C₈×C₁₁	—	4	4	no	—
59	C₄²×C₁₁	C₄²	1	1	yes	characteristic
60	C₄²×C₁₁	C₄²	1	2	yes	—
61	C₄²×C₁₁	C₄²	1	1	yes	characteristic
62	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
63	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
64	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
66	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
67	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
69	#4318	—	4	8	no	—
70	C₂×C₁₁⋊C₈	—	2	8	no	—
71	#2920	—	11	2	no	—
72	C₂×#431	D₁₁	1	1	yes	characteristic
73	#1293	—	11	4	no	—
74	C₂³×C₁₁	—	2	2	no	—
75	C₂³×C₁₁	—	4	1	no	—
76	C₂³×C₁₁	—	4	1	no	—
77	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
78	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₁	—	2	2	no	—
80	C₂×C₄×C₁₁	—	2	4	no	—
81	C₂×C₄×C₁₁	—	2	2	no	—
82	C₂×C₄×C₁₁	—	2	4	no	—
83	C₂×C₄×C₁₁	—	2	4	no	—
84	C₂×C₄×C₁₁	—	2	4	no	—
85	C₂×C₄×C₁₁	—	2	2	no	—
86	C₂×C₄×C₁₁	—	4	2	no	—
87	C₂×C₄×C₁₁	—	4	1	no	—
88	C₂×C₄×C₁₁	—	4	2	no	—
89	C₂×C₄×C₁₁	—	4	1	no	—
90	C₂×C₄×C₁₁	#95	1	2	yes	—
91	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
92	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
93	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
94	C₂×C₄×C₁₁	#95	1	2	yes	—
95	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
96	C₂×C₄×C₁₁	#108	1	4	yes	—
97	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
98	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
99	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₈×C₁₁	—	4	4	no	—
101	C₁₁⋊C₈	—	4	8	no	—
102	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
103	#432	—	11	4	no	—
104	#432	—	22	2	no	—
105	#431	—	2	2	no	—
106	#431	—	2	2	no	—
107	#431	—	11	4	no	—
108	#431	—	22	2	no	—
109	#423	—	22	2	no	—
110	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
111	#407	—	11	4	no	—
112	C₂×C₂²⋊C₈	C₂×D₁₁	1	2	yes	—
113	C₄×M₁₆	—	22	2	no	—
114	C₂×C₄×C₈	Dic₁₁	1	2	yes	—
115	C₂²×C₁₁	—	2	1	no	—
116	C₂²×C₁₁	—	2	1	no	—
117	C₂²×C₁₁	—	2	2	no	—
118	C₂²×C₁₁	—	2	2	no	—
119	C₂²×C₁₁	—	2	2	no	—
120	C₂²×C₁₁	—	4	4	no	—
121	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
122	C₂²×C₁₁	C₂×#108	1	2	yes	—
123	C₄×C₁₁	—	2	2	no	—
124	C₄×C₁₁	—	2	1	no	—
125	C₄×C₁₁	—	2	1	no	—
126	C₄×C₁₁	—	2	1	no	—
127	C₄×C₁₁	—	2	1	no	—
128	C₄×C₁₁	—	2	2	no	—
129	C₄×C₁₁	#338	1	2	yes	—
130	C₄×C₁₁	#341	1	4	yes	—
131	C₄×C₁₁	#410	1	2	yes	—
132	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
133	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
134	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
135	C₂×M₁₆	—	22	4	no	—
136	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
137	C₂×C₄²	C₄×D₁₁	1	2	yes	—
138	C₂×C₄²	C₄×D₁₁	1	2	yes	—
139	C₂×C₄²	D₄₄	1	1	yes	characteristic
140	C₂×C₄²	D₄₄	1	1	yes	characteristic
141	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
142	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
143	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
144	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
145	C₄⋊C₈	—	2	4	no	—
146	C₄⋊C₈	—	22	4	no	—
147	C₄⋊C₈	—	22	4	no	—
148	C₂²⋊C₈	—	2	4	no	—
149	C₂²⋊C₈	—	11	8	no	—
150	C₂²⋊C₈	—	22	4	no	—
151	#97	—	22	4	no	—
152	C₄×C₈	—	2	2	no	—
153	C₄×C₈	—	2	2	no	—
154	C₄×C₈	—	22	4	no	—
155	C₂×C₁₁	—	2	2	no	—
156	C₂×C₁₁	—	4	2	no	—
157	C₂×C₁₁	C₂×#338	1	1	yes	characteristic
158	C₂×C₁₁	C₂×#341	1	1	yes	characteristic
159	C₂×C₁₁	#1740	1	1	yes	characteristic
160	C₂⁴	C₂×Dic₂₂	1	1	yes	characteristic
161	C₂²×C₄	—	2	4	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	4	2	no	—
164	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
165	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
166	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
167	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
168	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
169	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
170	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
171	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
172	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
173	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
174	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
175	C₂²×C₄	C₂×C₂²⋊D₁₁	1	2	yes	—
176	M₁₆	—	44	8	no	—
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	4	4	no	—
179	C₂×C₈	—	22	8	no	—
180	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
181	C₄²	C₄×Dic₁₁	1	2	yes	—
182	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
183	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
184	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
185	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
186	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
187	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
188	C₄²	C₂²⋊Dic₁₁	1	2	yes	—
189	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
190	C₁₁	#8006	1	1	yes	characteristic, complemented, Sylow
191	C₂³	—	2	2	no	—
192	C₂³	—	4	1	no	—
193	C₂³	—	4	1	no	—
194	C₂³	C₂×Dic₁₁⋊C₄	1	2	yes	—
195	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	#66883	1	4	yes	—
208	C₂×C₄	C₁₁⋊#95	1	2	yes	—
209	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
210	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
211	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
212	C₂×C₄	C₁₁⋊#95	1	2	yes	—
213	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
214	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
215	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	2	yes	—
216	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
217	C₈	—	4	4	no	—
218	C₈	—	44	8	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	2	no	—
222	C₂²	—	2	2	no	—
223	C₂²	—	2	2	no	—
224	C₂²	—	4	4	no	—
225	C₂²	C₂×#66883	1	2	yes	—
226	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
227	C₄	—	2	2	no	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	2	no	—
232	C₄	—	2	1	no	—
233	C₄	#10622190	1	4	yes	—
234	C₄	C₁₁⋊#338	1	2	yes	—
235	C₄	#10622853	1	2	yes	—
236	C₂	—	2	2	no	—
237	C₂	—	4	2	no	—
238	C₂	C₂×C₁₁⋊#338	1	1	yes	characteristic
239	C₂	C₂×#10622190	1	1	yes	characteristic
240	C₂	#13068349	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₁₁⋊#95
commutator	C₂×C₄×C₁₁	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₁
Fitting	C₂×C₁₁×#431	C₂
socle	C₂²×C₁₁	C₂×#95
prime radical	C₂⁴×C₁₁	C₂×Q₈
cosocle	C₂³×C₄×C₁₁	C₂³
hypercenter	C₂×#431	D₁₁
hypocenter	C₁₁	#8006
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
190. C₁₁	#8006	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13077249	2
#13066493	2
C₂×C₁₁×#431	2
#8006	11